Assuming you can read/access the other person's repository - yes, you can. There are several ways to do so, for example:
Add a remote, and pull/fetch from it
Add a remote for the other user, merge in the changes and then push to your own repository:
cd /my/repo
git checkout master
git remote add otheruser https://github.com/otheruser/repo.git
git fetch otheruser
git merge otheruser/branch
Treat as a "manual" pull request
Github has a help page demonstrating how to do this:
cd /my/repo
git checkout master
git pull https://github.com/otheruser/repo.git branchname
git push origin master
Both of the above do the same thing - retrieve the branch history from a different repository and add the new commits to your own local repository (from there - just git push to update your own remote repository).